Stir together miso and 2 tablespoon butter. Discard turnip stems and coarsely chop leaves. Halve turnips (leave whole if tiny) and put in a 12-inch heavy skillet along with water, mirin, remaining tablespoon butter, and 1/8 teaspoon salt. Bring to a boil over medium-high heat, then boil, covered, 10 minutes. Add greens by handfuls, turning and stirring with tongs and adding more as volume in skillet reduces. Cover and cook 1 minute. Uncover and continue boiling, stirring occasionally, until turnips are tender and liquid is reduced to a glaze, about 5 minutes. Stir in miso butter and cook 1 minute.